Applied mathematics involves the application of mathematics to problems which arise in various areas, e.g., science, engineering or other diverse areas, and/or the development of new or improved methods to meet the challenges of new problems. We view applied math as the application of mathematics to real-world problems with the dual goal of explaining observed phenomena and predicting new, as yet unobserved, phenomena. Therefore, the emphasis is on both the mathematics, e.g. the development of new methods to meet the challenges of new problems, and the real world. The problems come from various applications, such as physical and biological sciences, engineering, and social sciences. Their solutions require knowledge of various branches of mathematics, such as analysis, differential equations, and stochastics, utilizing analytical and numerical methods. Very often our faculty members and students interact directly with experimentalists to see their research results come to life. Applied Mathematics has a profound impact on our daily lives. Whether it is weather forecasts, search engines, climate research, secure online shopping, or movie recommendations, none of these would work the way they do without algorithms and tools from the mathematical sciences. applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability. These areas of mathematics related directly to the development of Newtonian physics, and in fact, the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. This history left a pedagogical legacy in the United States: until the early 20th century, subjects such as classical mechanics were often taught in applied mathematics departments at American universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments. Engineering and computer science departments have traditionally made use of applied mathematics.
Optimization
It is a type of applied mathematics and the optimizing processes is one of the most powerful approaches in process integration. "Best" is a term used in optimization to describe the most advantageous option among a set of feasible alternatives mathematical modeling and numerical simulation. A mathematical model is a representation of physical reality that can be analyzed and calculated. We can compute the using numerical simulation,
calculate a model's solution on a computer in order to make a virtual duplicate of physical reality.
PDEs (partial differential equations) or multivariable differential equations will be our major modeling tool in this inquiry (time and space, for example).
Applied mathematics has a third fundamental feature: the mathematical study of models.
Mathematical analysis is a necessary step It is possible to get some severe shocks from numerical solutions to physical models.
A detailed understanding of the underlying mathematical ideas is required to fully appreciate them. and
Nonlinear problems and applications are the driving force behind applied mathematics.
difficulties that do not have any random or stochastic aspects. Finally, something must be done in order for this to work.
In our efforts to be simple and understandable, we may occasionally use ambiguous language.
in our use of mathematics. We may ensure the more discerning reader that
an example of modeling that leads to the equation for heat flow.
Numerical algorithms must be utilized. This goal is to show and analyze several algorithms that help us to better understand the world around us.
To tackle real-world problems, all of the algorithms covered here may be put to work
computer-aided to specific optimization issues.
All of these algorithms are iterative in nature, beginning with a predetermined initial 〖(u〗_0) condition.
Each approach creates a sequence (U_n) n ∈ N that converges under certain conditions
The applications in life using Dynamic optimization
1- Dynamic of Floating Offshore Wind Turbines
Floating offshore wind turbines have the potential to harness the vast deepwater wind resource and provide renewable energy to a sizable portion of the global population. Dynamical models were required to determine the viability of various concepts for f loating wind turbines by taking into account wind turbine dynamics (including wind f low, aerodynamics, elasticity, and control), incident wave dynamics, sea current dynamics, hydrodynamics, and mooring dynamics of the floating platform. Finance and technology. These dynamic turbines are equipped with the features needed to conduct load analyses for different rotor assemblies, tower, support platform, and mooring system configurations. Excitation of the incident wave from linear diffraction in normal or irregular seas; linear hydrostatic recovery process; nonlinear viscous clouds; linear wave radiation contributes mass and damping, and there are also free-surface memory effects. In response to the interaction between the mooring lines and the sea floor, a semi-fixed mooring line unit has been developed. You can count this as one of the dynamic programs
2- The engine in a car provides the power necessary for the car to accelerate and move forward. The dynamic force exerted by the car engine as it moves from one location to another over time is the driving force. Forces that change position over time are called dynamic forces
The applications in life using control optimization
1- COVID-19
The COVID-19 pandemic has started an unprecedented series of international choices. Without any reliable vaccines or drug treatments, governments have resorted to non-drug methods including isolation, quarantine, and lockdowns to slow the spread of the disease. Although these measures are useful in reducing the spread of the virus and buying the healthcare system some time to adjust, they can be very costly economically and socially, and over longer periods the public is less likely to comply. Pharmaceutical interventions, such as vaccination or therapy, have been extensively explored for their potential to shed light on optimal control problems for systems governed by the SIR or the SEIR model. Non-drug interventions have been extensively researched for a control consisting of isolates acting only on infected subjects in the context of optimal control problems. Given that there is an undetected incubation period, non-drug therapies can range from a mild mitigation policy to a strong suppression policy. The suppression effort ”seeks to halt the spread of the epidemic by reducing the number of new cases and ensuring that the current low number of cases remains in place indefinitely.” Restrictions on travel, closures of schools and businesses, bans on social gatherings, and “shelter in place” orders are all tools of oppression. We use an optimal control approach to demonstrate that a single DOI, that is, a very short period of isolation, is the best course of action.he evolution of the system is governed by the following set of coupled nonlinear ordinary differential equations
2-Energy Management
Powerful optimization received a great deal of focus in the area of energy management. From crude oil production to refined product demand and market prices, the oil industry as a whole can benefit from a strategic planning approach. Reducing local cost requires attention to both unit commitment and economic phases of transportation. Within the organisation, production uses most of the energy. The importance of production planning and management increases accordingly. Plan, control and manage all activities involved in creating a product, including those relating to time, space, quantity and operation. The manufacturing planner is responsible for organizing production processes to maximize and optimize the use of resources. As the structure of energy production changes in the near future, there will be a greater need for storage facilities. Limited energy storage is a concern that must be considered in production planning and control. Energy can theoretically be stored in three different ways: electrically, mechanically, and chemically
by Dr. Ammar imad nadhim nomi